On the steady shear flow of a dipolar fluid in a porous half-space

The plate-driven flow of an incompressible, homogeneous, dipolar fluid in a porous half-space is studied. The exact solution to this problem, which corresponds to the porous media version of the steady-state Stokes’ first problem for dipolar fluids, is obtained and an in-depth analytical and numerical investigation is carried out. Specifically, special cases of the physical parameters are determined and investigated, asymptotic results are given, physical interpretation(s) are discussed, and connections to other areas are noted.Most significantly, the analysis shows the following: (I) that a back flow can occur; (II) the flow velocity is predicted to exceed that of the (driving) plate for certain values of the physical parameters; (III) that a connection exists between the golden ratio and the solution presented here; (IV) that the flow is mathematically equivalent to the unforced motion of a damped harmonic oscillator.